11 citations · 32 across the 13 of their papers we have counts for
14 papers
Uniform spectral gap of scl in -orbifolds
Lvzhou Chen, Nicolaus Heuer
We show a uniform spectral gap of stable commutator length for all compact hyperbolic -orbifolds relative to the peripheral subgroups. Except for the case of a sphere with three…
The Wiegold problem and free products of left-orderable groups
Lvzhou Chen, Yash Lodha
A group has normal rank (or weight) greater than one if no single element normally generates the group. The Wiegold problem from 1976 asks about the existence of a finitely generat…
Irrational rotations and 2-filling rays
Lvzhou Chen, Alexander J. Rasmussen
We study a skew product transformation associated to an irrational rotation of the circle [0,1]/~. This skew product keeps track of the number of times an orbit of the rotation lan…
The Kervaire conjecture and the minimal complexity of surfaces
Lvzhou Chen
The Kervaire conjecture asserts that adding a generator and then a relator to a nontrivial group always results in a nontrivial group. We introduce new methods from stable commutat…
A height gap in and almost laws
Lvzhou Chen, Sebastian Hurtado, Homin Lee
E. Breuillard showed that finite subsets of matrices in generating non-virtually solvable groups have normalized height ,…
Normal subgroups of big mapping class groups
Danny Calegari, Lvzhou Chen
Let S be a surface and let Mod(S,K) be the mapping class group of S permuting a Cantor subset K of S. We prove two structure theorems for normal subgroups of Mod(S,K). (Purity:) if…
Stable Torsion Length
Chloe I. Avery, Lvzhou Chen
The stable torsion length in a group is the stable word length with respect to the set of all torsion elements. We show that the stable torsion length vanishes in crystallographic…
Stable commutator length in right-angled Artin and Coxeter groups
Lvzhou Chen, Nicolaus Heuer
We establish a spectral gap for stable commutator length (scl) of integral chains in right-angled Artin groups (RAAGs). We show that this gap is not uniform, i.e. there are RAAGs a…
Laminations and 2-filling rays on infinite type surfaces
Lvzhou Chen, Alexander J. Rasmussen
The loop graph of an infinite type surface is an infinite diameter hyperbolic graph first studied in detail by Juliette Bavard. An important open problem in the study of infinite t…
Nielsen realization for infinite-type surfaces
Santana Afton, Danny Calegari, Lvzhou Chen +1
Given a finite subgroup G of the mapping class group of a surface S, the Nielsen realization problem asks whether G can be realized as a finite group of homeomorphisms of S. In 198…
Spectral gap of scl in graphs of groups and -manifolds
Lvzhou Chen, Nicolaus Heuer
Stable commutator length scl_G(g) of an element g in a group G is an invariant for group elements sensitive to the geometry and dynamics of G. For any group G acting on a tree, we…
Big mapping class groups and rigidity of the simple circle
Danny Calegari, Lvzhou Chen
Let denote the mapping class group of the plane minus a Cantor set. We show that every action of on the circle is either trivial or semi-conjugate to a unique minimal actio…
Spectral gap of scl in free products
Lvzhou Chen
Let be a free product of torsion-free groups, and let be any element not conjugate into a . Then scl. This generalizes, and gives a new pro…
Scl in free products
Lvzhou Chen
We study stable commutator length (scl) in free products via surface maps into a wedge of spaces. We prove that scl is piecewise rational linear if it vanishes on each factor of th…